Worksheet 4: Continuity and Derivatives with Limits
Final Review Part 1
1. Prove [pic]
2. Prove [pic] using the delta-epsilon definition of a limit
3. Write the delta-epsilon definition for a limit not existing.
4. An example of a function where the integral does not exist:
[pic]
5. A function that has no antiderivative: [pic]
6. Suppose the function [pic] is defined as [pic] when [pic]. If [pic] exists, find[pic] and [pic]
7. Find the domain, range, and derivative of[pic]
8. Find the derivative and second derivative of[pic]
9. Find the 1000th and 2000th derivatives of[pic]
10. Find the nth derivative of[pic]
11. True or false:
a. [pic]
b. [pic]
c. If [pic]and [pic], then [pic]
d. [pic], [pic] and [pic] implies that [pic] has an inflection point at x = 0
e. L’Hospital’s rule is equivalent to: if [pic], [pic]
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